TSTP Solution File: PUZ047-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ047-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:24:04 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ047-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.34 % Computer : n016.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sat Aug 26 22:33:42 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.20/0.42 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Take the following subset of the input axioms:
% 0.20/0.43 fof(thm100_1, negated_conjecture, p(south, south, south, south, start)).
% 0.20/0.43 fof(thm100_10, negated_conjecture, ![B, C, A2]: (p(north, A2, north, B, take_goat(C)) | ~p(south, A2, south, B, C))).
% 0.20/0.43 fof(thm100_11, negated_conjecture, ![A2_2, B2, C2]: (p(south, A2_2, south, B2, take_goat(C2)) | ~p(north, A2_2, north, B2, C2))).
% 0.20/0.43 fof(thm100_14, negated_conjecture, ![A2_2]: (p(north, south, north, north, take_cabbage(A2_2)) | ~p(south, south, north, south, A2_2))).
% 0.20/0.43 fof(thm100_16, negated_conjecture, ![A]: ~p(north, north, north, north, A)).
% 0.20/0.43 fof(thm100_3, negated_conjecture, ![A2_2]: (p(south, north, south, north, go_alone(A2_2)) | ~p(north, north, south, north, A2_2))).
% 0.20/0.43 fof(thm100_5, negated_conjecture, ![A2_2]: (p(south, south, north, south, go_alone(A2_2)) | ~p(north, south, north, south, A2_2))).
% 0.20/0.43 fof(thm100_6, negated_conjecture, ![A2_2]: (p(north, north, south, north, take_wolf(A2_2)) | ~p(south, south, south, north, A2_2))).
% 0.20/0.43
% 0.20/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.43 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (thm100_14): fresh10(X, X, Y) = true2.
% 0.20/0.43 Axiom 2 (thm100_3): fresh7(X, X, Y) = true2.
% 0.20/0.43 Axiom 3 (thm100_5): fresh5(X, X, Y) = true2.
% 0.20/0.43 Axiom 4 (thm100_6): fresh4(X, X, Y) = true2.
% 0.20/0.43 Axiom 5 (thm100_1): p(south, south, south, south, start) = true2.
% 0.20/0.43 Axiom 6 (thm100_11): fresh14(X, X, Y, Z, W) = true2.
% 0.20/0.43 Axiom 7 (thm100_10): fresh13(X, X, Y, Z, W) = true2.
% 0.20/0.43 Axiom 8 (thm100_14): fresh10(p(south, south, north, south, X), true2, X) = p(north, south, north, north, take_cabbage(X)).
% 0.20/0.43 Axiom 9 (thm100_3): fresh7(p(north, north, south, north, X), true2, X) = p(south, north, south, north, go_alone(X)).
% 0.20/0.43 Axiom 10 (thm100_5): fresh5(p(north, south, north, south, X), true2, X) = p(south, south, north, south, go_alone(X)).
% 0.20/0.43 Axiom 11 (thm100_6): fresh4(p(south, south, south, north, X), true2, X) = p(north, north, south, north, take_wolf(X)).
% 0.20/0.43 Axiom 12 (thm100_11): fresh14(p(north, X, north, Y, Z), true2, X, Y, Z) = p(south, X, south, Y, take_goat(Z)).
% 0.20/0.43 Axiom 13 (thm100_10): fresh13(p(south, X, south, Y, Z), true2, X, Y, Z) = p(north, X, north, Y, take_goat(Z)).
% 0.20/0.43
% 0.20/0.43 Goal 1 (thm100_16): p(north, north, north, north, X) = true2.
% 0.20/0.43 The goal is true when:
% 0.20/0.43 X = take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43
% 0.20/0.43 Proof:
% 0.20/0.43 p(north, north, north, north, take_goat(go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))))
% 0.20/0.43 = { by axiom 13 (thm100_10) R->L }
% 0.20/0.43 fresh13(p(south, north, south, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start))))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 9 (thm100_3) R->L }
% 0.20/0.43 fresh13(fresh7(p(north, north, south, north, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 11 (thm100_6) R->L }
% 0.20/0.43 fresh13(fresh7(fresh4(p(south, south, south, north, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 12 (thm100_11) R->L }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(p(north, south, north, north, take_cabbage(go_alone(take_goat(start)))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 8 (thm100_14) R->L }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(p(south, south, north, south, go_alone(take_goat(start))), true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 10 (thm100_5) R->L }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(fresh5(p(north, south, north, south, take_goat(start)), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 13 (thm100_10) R->L }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(fresh5(fresh13(p(south, south, south, south, start), true2, south, south, start), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 5 (thm100_1) }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(fresh5(fresh13(true2, true2, south, south, start), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 7 (thm100_10) }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(fresh5(true2, true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 3 (thm100_5) }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(fresh10(true2, true2, go_alone(take_goat(start))), true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 1 (thm100_14) }
% 0.20/0.43 fresh13(fresh7(fresh4(fresh14(true2, true2, south, north, take_cabbage(go_alone(take_goat(start)))), true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 6 (thm100_11) }
% 0.20/0.43 fresh13(fresh7(fresh4(true2, true2, take_goat(take_cabbage(go_alone(take_goat(start))))), true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 4 (thm100_6) }
% 0.20/0.43 fresh13(fresh7(true2, true2, take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 2 (thm100_3) }
% 0.20/0.43 fresh13(true2, true2, north, north, go_alone(take_wolf(take_goat(take_cabbage(go_alone(take_goat(start)))))))
% 0.20/0.43 = { by axiom 7 (thm100_10) }
% 0.20/0.43 true2
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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